At a temperature of roughly 1 K, ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ undergoes a transition from a normal Fermi liquid to a superconducting phase. Even while the former is relatively simple and well understood, the superconducting state has not even been understood after 25 years of study. More recently, it has been found that critical temperatures can be enhanced by the application of uniaxial strain, up to a critical strain, after which it falls off. In this work, we take an “instability” approach and seek divergences in susceptibilities. This provides an unbiased way to distinguish tendencies to competing ground states. We show that in the unstrained compound, the singlet and triplet instabilities of the normal Fermi liquid phase are closely spaced. Under uniaxial strain, electrons residing on all orbitals contributing to the Fermiology become more coherent, while the electrons of the Ru-$d_{xy}$ character become heavier, and the electrons of the Ru-$d_{xz,yz}$ characters become lighter. In the process, Im $\chi (\mathbf{q},\omega )$ increases rapidly around $\mathbf{q} = (0.3,0.3,0)2\pi /a$ and $\mathbf{q} = (0.5,0.25,0)2\pi /a$, while it gets suppressed at all other commensurate vectors, in particular at $\mathbf{q} = 0$, which is essential for spin-triplet superconductivity. We observe that the magnetic anisotropy under strain drops smoothly, which is concomitant with the increment in singlet instability. Thus, the triplet superconducting instability remains the lagging instability of the system, and the singlet instability enhances under strain, leading to a large energy-scale separation between these competing instabilities. However, since this happens even without spin-orbit coupling, we believe it is primarily the enhancement in the spin fluctuation glue around quasi-anti-ferromagnetic vectors that drives the Cooper pairing instead of the magnetic anisotropy. At large strain, an instability to a spin density wave overtakes the superconducting one. The analysis relies on a high-fidelity, ab initio description of the one-particle properties and two-particle susceptibilities, based on the quasiparticle self-consistent GW approximation augmented by dynamical mean field theory. This approach is described and its high fidelity confirmed by comparing to observed one- and two-particle properties.

Lanthanide hydrogen-rich materials have long been considered as one of the candidates with high-temperature superconducting properties in condensed matter physics, and have been a popular topic of research. Attempts to investigate the effects of different compositions of lanthanide hydrogen-rich materials are ongoing, with predictions and experimental studies in recent years showing that substances such as LaH${}_{10}$, CeH${}_9$, and LaH${}_{16}$ exhibit extremely high superconducting temperatures between 150–250 GPa. In particular, researchers have noted that, in those materials, a rise in the f orbit character at the Fermi level combined with the presence of hydrogen vibration modes at the same low energy scale will lead to an increase in the superconducting transition temperature. Here, we further elaborate on the effect of the ratios of lanthanide to hydrogen in these substances with the aim of bringing more clarity to the study of superhydrides in these extreme cases by comparing a variety of lanthanide hydrogen-rich materials with different ratios using the dynamical mean-field theory (DMFT) method, and provide ideas for later structural predictions and material property studies.

Quantum computing platforms rely on simulators for modelling circuit behaviour prior to hardware execution, where inconsistencies can lead to costly errors. While existing formal validation methods typically target specific compiler components to manage state explosion, they often miss critical bugs. Meanwhile, conventional testing lacks systematic exploration of corner cases and realistic execution scenarios, resulting in both false positives and negatives. We present FuzzQ, a novel framework that bridges this gap by combining formal methods with structured test generation and fuzzing for quantum simulators. Our approach employs differential benchmarking complemented by mutation testing and invariant checking. At its core, FuzzQ utilises our Alloy-based formal model of QASM 3.0, which encodes the semantics of quantum circuits to enable automated analysis and to generate structurally diverse, constraint-guided quantum circuits with guaranteed properties. We introduce several test oracles to assess both Alloy’s modelling of QASM 3.0 and simulator correctness, including invariant-based checks, statistical distribution tests, and a novel cross-simulator unitary consistency check that verifies functional equivalence modulo global phase, revealing discrepancies that standard statevector comparisons fail to detect in cross-platform differential testing. We evaluate FuzzQ on both Qiskit and Cirq, demonstrating its platform-agnostic effectiveness. By executing over 800,000 quantum circuits to completion, we assess throughput, code and circuit coverage, and simulator performance metrics, including sensitivity, correctness, and memory overhead. Our analysis revealed eight simulator bugs, six previously undocumented. We also outline a path for extending the framework to support mixed-state simulations under realistic noise models.

We present AccelerQ, a framework for automatically tuning quantum eigensolver (QE) implementations–these are quantum programs implementing a specific QE algorithm–using machine learning and search-based optimisation. Rather than redesigning quantum algorithms or manually tweaking the code of an already existing implementation, AccelerQ treats QE implementations as black-box programs and learns to optimise their hyperparameters to improve accuracy and efficiency by incorporating search-based techniques and genetic algorithms (GA) alongside ML models to efficiently explore the hyperparameter space of QE implementations and avoid local minima. Our approach leverages two ideas: 1) train on data from smaller, classically simulable systems, and 2) use program-specific ML models, exploiting the fact that local physical interactions in molecular systems persist across scales, supporting generalisation to larger systems. We present an empirical evaluation of AccelerQ on two fundamentally different QE implementations: ADAPT-QSCI and QCELS. For each, we trained a QE predictor model, a lightweight XGBoost Python regressor, using data extracted classically from systems of up to 16 qubits. We deployed the model to optimise hyperparameters for executions on larger systems of 20-, 24-, and 28-qubit Hamiltonians, where direct classical simulation becomes impractical. We observed a reduction in error from 5.48% to 5.3% with only the ML model and further to 5.05% with GA for ADAPT-QSCI, and from 7.5% to 6.5%, with no additional gain with GA for QCELS. Given inconclusive results for some 20- and 24-qubit systems, we recommend further analysis of training data concerning Hamiltonian characteristics. Nonetheless, our results highlight the potential of ML and optimisation techniques for quantum programs and suggest promising directions for integrating software engineering methods into quantum software stacks.

The world obeys quantum physics and quantum computing presents an alternative way to map physical problems to systems that follow the same laws. Such computation fundamentally constitutes a better way to understand the most challenging quantum problems. One such problem is the accurate simulation of highly correlated quantum systems. Still, modern-day quantum hardware has limitations and only allows for the modeling of simple systems. Here, we present for the first time a quantum computer model simulation of a complex hemocyanin molecule, which is an important respiratory protein involved in various physiological processes and is also used as a key component in therapeutic vaccines for cancer. To characterize the mechanism by which hemocyanin transports oxygen, variational quantum eigensolver (VQE) and quantum embedding methods are used in the context of dynamic mean field theory to solve the Anderson impurity model (AIM). Finally, it is concluded that the magnetic structure of hemocyanin is largely influenced by the many-body correction and that the computational effort for solving correlated electron systems could be substantially reduced with the introduction of quantum computing algorithms. We encourage the use of the Hamiltonian systems presented in this paper as a benchmark for testing quantum computing algorithms’ efficiency for chemistry applications.